TSTP Solution File: KLE072+1 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : KLE072+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 05:25:10 EDT 2023
% Result : Theorem 0.64s 0.70s
% Output : CNFRefutation 0.64s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : KLE072+1 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 0.12/0.34 % Computer : n002.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Tue Aug 29 11:33:05 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.20/0.56 start to proof:theBenchmark
% 0.64/0.69 %-------------------------------------------
% 0.64/0.69 % File :CSE---1.6
% 0.64/0.69 % Problem :theBenchmark
% 0.64/0.69 % Transform :cnf
% 0.64/0.69 % Format :tptp:raw
% 0.64/0.69 % Command :java -jar mcs_scs.jar %d %s
% 0.64/0.69
% 0.64/0.69 % Result :Theorem 0.080000s
% 0.64/0.69 % Output :CNFRefutation 0.080000s
% 0.64/0.69 %-------------------------------------------
% 0.64/0.70 %------------------------------------------------------------------------------
% 0.64/0.70 % File : KLE072+1 : TPTP v8.1.2. Released v4.0.0.
% 0.64/0.70 % Domain : Kleene Algebra (Domain Semirings)
% 0.64/0.70 % Problem : Domain elements satisfy the first axiom of Kleene modules
% 0.64/0.70 % Version : [Hoe08] axioms.
% 0.64/0.70 % English :
% 0.64/0.70
% 0.64/0.70 % Refs : [DMS06] Desharnais et al. (2006), Kleene Algebra with Domain
% 0.64/0.70 % : [Lei06] Leiss (2006), Kleene Modules and Linear Languages
% 0.64/0.70 % : [DS08] Desharnais & Struth (2008), Modal Semirings Revisited
% 0.64/0.70 % : [Hoe08] Hoefner (2008), Email to G. Sutcliffe
% 0.64/0.70 % Source : [Hoe08]
% 0.64/0.70 % Names :
% 0.64/0.70
% 0.64/0.70 % Status : Theorem
% 0.64/0.70 % Rating : 0.14 v7.5.0, 0.16 v7.4.0, 0.07 v7.3.0, 0.14 v7.1.0, 0.13 v6.4.0, 0.19 v6.3.0, 0.08 v6.2.0, 0.16 v6.1.0, 0.23 v6.0.0, 0.17 v5.5.0, 0.15 v5.4.0, 0.18 v5.3.0, 0.30 v5.2.0, 0.20 v5.1.0, 0.19 v5.0.0, 0.21 v4.1.0, 0.17 v4.0.0
% 0.64/0.70 % Syntax : Number of formulae : 18 ( 17 unt; 0 def)
% 0.64/0.70 % Number of atoms : 19 ( 18 equ)
% 0.64/0.70 % Maximal formula atoms : 2 ( 1 avg)
% 0.64/0.70 % Number of connectives : 1 ( 0 ~; 0 |; 0 &)
% 0.64/0.70 % ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% 0.64/0.70 % Maximal formula depth : 4 ( 3 avg)
% 0.64/0.70 % Maximal term depth : 5 ( 2 avg)
% 0.64/0.70 % Number of predicates : 2 ( 1 usr; 0 prp; 2-2 aty)
% 0.64/0.70 % Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% 0.64/0.70 % Number of variables : 31 ( 31 !; 0 ?)
% 0.64/0.70 % SPC : FOF_THM_RFO_SEQ
% 0.64/0.70
% 0.64/0.70 % Comments : Equational encoding
% 0.64/0.70 %------------------------------------------------------------------------------
% 0.64/0.70 %---Include axioms for domain semiring
% 0.64/0.70 include('Axioms/KLE001+0.ax').
% 0.64/0.70 %---Include axioms for domain
% 0.64/0.70 include('Axioms/KLE001+5.ax').
% 0.64/0.70 %------------------------------------------------------------------------------
% 0.64/0.70 fof(goals,conjecture,
% 0.64/0.70 ! [X0,X1,X2] : domain(multiplication(addition(X0,X1),domain(X2))) = addition(domain(multiplication(X0,domain(X2))),domain(multiplication(X1,domain(X2)))) ).
% 0.64/0.70
% 0.64/0.70 %------------------------------------------------------------------------------
% 0.64/0.70 %-------------------------------------------
% 0.64/0.70 % Proof found
% 0.64/0.70 % SZS status Theorem for theBenchmark
% 0.64/0.70 % SZS output start Proof
% 0.64/0.70 %ClaNum:29(EqnAxiom:10)
% 0.64/0.70 %VarNum:65(SingletonVarNum:30)
% 0.64/0.70 %MaxLitNum:2
% 0.64/0.70 %MaxfuncDepth:4
% 0.64/0.70 %SharedTerms:17
% 0.64/0.70 %goalClause: 27
% 0.64/0.70 %singleGoalClaCount:1
% 0.64/0.70 [11]E(f2(a1),a1)
% 0.64/0.70 [27]~E(f3(f2(f4(a5,f2(a6))),f2(f4(a7,f2(a6)))),f2(f4(f3(a5,a7),f2(a6))))
% 0.64/0.70 [12]E(f4(x121,a1),a1)
% 0.64/0.70 [13]E(f4(a1,x131),a1)
% 0.64/0.70 [14]E(f3(x141,a1),x141)
% 0.64/0.70 [15]E(f4(x151,a8),x151)
% 0.64/0.70 [16]E(f4(a8,x161),x161)
% 0.64/0.70 [17]E(f3(x171,x171),x171)
% 0.64/0.70 [18]E(f3(f2(x181),a8),a8)
% 0.64/0.70 [22]E(f3(x221,f4(f2(x221),x221)),f4(f2(x221),x221))
% 0.64/0.70 [19]E(f3(x191,x192),f3(x192,x191))
% 0.64/0.70 [20]E(f2(f3(x201,x202)),f3(f2(x201),f2(x202)))
% 0.64/0.70 [21]E(f2(f4(x211,f2(x212))),f2(f4(x211,x212)))
% 0.64/0.70 [23]E(f3(f3(x231,x232),x233),f3(x231,f3(x232,x233)))
% 0.64/0.70 [24]E(f4(f4(x241,x242),x243),f4(x241,f4(x242,x243)))
% 0.64/0.70 [25]E(f3(f4(x251,x252),f4(x251,x253)),f4(x251,f3(x252,x253)))
% 0.64/0.70 [26]E(f3(f4(x261,x262),f4(x263,x262)),f4(f3(x261,x263),x262))
% 0.64/0.70 [28]~P1(x281,x282)+E(f3(x281,x282),x282)
% 0.64/0.70 [29]P1(x291,x292)+~E(f3(x291,x292),x292)
% 0.64/0.70 %EqnAxiom
% 0.64/0.70 [1]E(x11,x11)
% 0.64/0.70 [2]E(x22,x21)+~E(x21,x22)
% 0.64/0.70 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.64/0.70 [4]~E(x41,x42)+E(f2(x41),f2(x42))
% 0.64/0.70 [5]~E(x51,x52)+E(f4(x51,x53),f4(x52,x53))
% 0.64/0.70 [6]~E(x61,x62)+E(f4(x63,x61),f4(x63,x62))
% 0.64/0.70 [7]~E(x71,x72)+E(f3(x71,x73),f3(x72,x73))
% 0.64/0.70 [8]~E(x81,x82)+E(f3(x83,x81),f3(x83,x82))
% 0.64/0.70 [9]P1(x92,x93)+~E(x91,x92)+~P1(x91,x93)
% 0.64/0.70 [10]P1(x103,x102)+~E(x101,x102)+~P1(x103,x101)
% 0.64/0.70
% 0.64/0.70 %-------------------------------------------
% 0.64/0.70 cnf(31,plain,
% 0.64/0.70 (P1(x311,x311)),
% 0.64/0.70 inference(scs_inference,[],[11,17,2,29])).
% 0.64/0.70 cnf(44,plain,
% 0.64/0.70 (~E(f2(f4(f3(a5,a7),f2(a6))),f3(f2(f4(a5,f2(a6))),f2(f4(a7,f2(a6)))))),
% 0.64/0.70 inference(scs_inference,[],[27,2])).
% 0.64/0.70 cnf(106,plain,
% 0.64/0.70 (P1(x1061,f4(x1061,a8))),
% 0.64/0.70 inference(scs_inference,[],[15,31,9])).
% 0.64/0.70 cnf(129,plain,
% 0.64/0.70 (~E(f2(f4(f3(a5,a7),f2(a6))),f2(f3(f4(a5,f2(a6)),f4(a7,f2(a6)))))),
% 0.64/0.70 inference(scs_inference,[],[18,20,44,4,3])).
% 0.64/0.70 cnf(135,plain,
% 0.64/0.70 (E(f3(x1351,f3(f2(x1352),a8)),f3(x1351,a8))),
% 0.64/0.70 inference(scs_inference,[],[18,20,44,106,4,3,28,7,6,8])).
% 0.64/0.70 cnf(147,plain,
% 0.64/0.70 (~E(f2(f3(f4(a5,f2(a6)),f4(a7,f2(a6)))),f2(f4(f3(a5,a7),f2(a6))))),
% 0.64/0.70 inference(scs_inference,[],[129,135,29,4,2])).
% 0.64/0.70 cnf(157,plain,
% 0.64/0.70 ($false),
% 0.64/0.70 inference(scs_inference,[],[26,147,4]),
% 0.64/0.70 ['proof']).
% 0.64/0.70 % SZS output end Proof
% 0.64/0.70 % Total time :0.080000s
%------------------------------------------------------------------------------